A residue, broadly, is anything left behind by a reaction or event.
In complex analysis, the residue is a complex number which describes the behavior of path integrals of a meromorphic function around a singularity. See residue (complex analysis).
In modular arithmetic, the residue of an integer n to base b is the remainder r after the largest multiple mb of b no greater than n has been subtracted from n (if n < 0, one adds multiples of b just sufficient to make the result non-negative). The residues modulo (to the base) b form a ring.
In molecular biology, particularly with enzymes, a residue refers to a specific amino acid. For example one might say: "the histadine residue is considered to be basic due to its imidazole ring". Note that a residue is different from a moiety, which, in the above example would consistute the imidazole ring or "the imidazole moiety".
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